Q: The ratio of efficiency of A is to C is 5:3. The ratio of number of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C started the work and left after 2 days. The number of days taken by A to finish the remaining work is:
Solution: A : C
Efficiency 5 : 3
No of days 3x : 5x
Given that, 5x-6 =3x => x = 3
Number of days taken by A = 9
Number of days taken by C = 15
B : C
Days 2 : 3
Therefore, Number of days taken by B = 10
Work done by B and C in initial 2 days = 2110+115= 1/3
Thus, Rest work =2/3
Number of days required by A to finish 2/3 work = (2/3) x 9 = 6 days Q: Namitha sold a powerbank which is at the cost of Rs. 1950 at a loss of 25%. Find at what cost will she have to sell it to get a profit of 25%?
Solution: Let the Cost price of the powerbank = Rs. P But given that by selling it at Rs. 1950, it gives a loss of 25% => P x 75100 = 1950=>P = 1950 x 10075 = Rs. 2600Now, to get a profit of 25% Selling Price = 2600 x 125100 = Rs. 3250.
Q: A shopkeeper sells two articles at Rs.1000 each, making a profit of 30% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes ?
Solution: SP of first article = 1000Profit = 30%CP = (SP)x[100/(100+P)] = 10000/13 SP of second article = 1000Loss = 20%CP = (SP)x[100/(100-L)] = 5000/4 = 1250 Total SP = 2000 Total CP = 10000/13 + 1250 = 2019.23 CP is more than SP, he makes a loss. Loss = CP-SP = 2019.23 - 2000 = 19.23Loss Percent = [(19.23)/(2019.23)]x100 = 0.95 %.
Q: If Arun’s birthday is on May 25 which is Monday and his sister’s birthday is on July 13. Which day of the week is his sister’s birthday?
Solution: Reference day : May 25th Monday Days from May 25th to July 13 = 6 + 30 +13 = 49 No of odd days : 49/7 = 0
Q: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
Solution: Milk = 3/5 * 20 = 12 liters, water = 8 liters If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters. Remaining milk = 12 - 6 = 6 liters Remaining water = 8 - 4 = 4 liters 10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters. The ratio of milk and water in the new mixture = 16:4 = 4:1 If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters. Amount of water removed = 2 liters. Remaining milk = (16 - 8) = 8 liters. Remaining water = (4 -2) = 2 liters. The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
Q: A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
Solution: Let the initial quantity of milk in the vessel be T litres. Let us say y liters of the mixture is taken out and replaced by water for n times, alternatively. Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T For the given problem, T = 90, y = 9 and n = 2. Hence, quantity of milk finally in the vessel = [(90 - 9)/90]2 (90) = 72.9 litres.
Q: In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
Solution: 1 x 40 x x = 40 x 1 x 40
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